Elastic moduli of model random three-dimensional closed-cell cellular solids

Roberts, Anthony P.; Garboczi, Edward J.

doi:10.1016/s1359-6454(00)00314-1

Cited by 423 publications

(193 citation statements)

References 26 publications

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“…(2) and the resultant n values obtained in this study are shown in Table 4. These values are consistent with the data presented in the literature on the modulus of porous materials [23]. It is clear that the inclusion of Bioglass® particles has only a limited effect on the n value, as the calculated n value for samples with 0, 2 and 15 vol.% Bioglass® have a coefficient of variation of 2.4% and 4.9% when considering axial and transversal loading, respectively, by using the Ishai-Cohen model for the composite foams.…”

Section: Theoretical Modellingsupporting

confidence: 90%

“…The constants C and n depend on the microstructure of the foam scaffold. The value of n generally lies in the range 1 < n < 4 giving a wide range of values for E/E 0 at a given density [23]. It has been suggested that for closed-cell porous systems n should have a value in the range of 1 < n < 2.…”

Section: Theoretical Modellingmentioning

confidence: 99%

“…It has been suggested that for closed-cell porous systems n should have a value in the range of 1 < n < 2. In their model, Roberts and Garboczi [23] found that if more than 70% of the cell faces are removed, n should increase to 2, indicating that edge bending becomes the dominant mechanism of deformation.…”

Section: Theoretical Modellingmentioning

confidence: 99%

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Mechanical properties of highly porous PDLLA/Bioglass® composite foams as scaffolds for bone tissue engineering

et al. 2005

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This study developed highly porous degradable composites as potential scaffolds for bone tissue engineering. These scaffolds consisted of poly-D,L-lactic acid filled with 2 and 15 vol.% of 45S5 Bioglass® particles and were produced via thermally induced solid-liquid phase separation and subsequent solvent sublimation. The scaffolds had a bimodal and anisotropic pore structure, with tubular macro-pores of ~100 µm in diameter, and with interconnected micro-pores of ~10-50 µm in diameter. Quasi-static and thermal dynamic mechanical analysis carried out in compression along with thermogravimetric analysis was used to investigate the effect of Bioglass® on the properties of the foams. Quasi-static compression testing demonstrated mechanical anisotropy concomitant with the direction of the macro-pores. An analytical modelling approach was applied, which demonstrated that the presence of Bioglass® did not significantly alter the porous architecture of these foams and reflected the mechanical anisotropy which was congruent with the scanning electron microscopy investigation. This study found that the Ishai-Cohen and Gibson-Ashby models can be combined to predict the compressive modulus of the composite foams. The modulus and density of these complex foams are related by a power-law function with an exponent between 2 and 3.

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Section: Theoretical Modellingsupporting

confidence: 90%

Section: Theoretical Modellingmentioning

confidence: 99%

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Mechanical properties of highly porous PDLLA/Bioglass® composite foams as scaffolds for bone tissue engineering

et al. 2005

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“…A equação P se torna a equação O quando C = 1 e n = 2. Numa simulação com células abertas de uma esponja do tipo tetrakaidecaedral, Roberts e Carboczi [19] obtiveram os valores de C = 0,93 e n = 2,04, para r/r 0 < 0,5, muito próximos dos valores 1 e 2, respectivamente.…”

Section: Dependência Com a Porosidadeunclassified

Relação entre porosidade e os módulos elásticos de esponjas cerâmicas produzidas via "gelcasting"

et al. 2004

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ResumoA técnica gelcasting , associada à aeração de suspensões cerâmicas, permite a produção de esponjas cerâmicas com uma larga faixa de porosidade. Esponjas à base de alumina foram produzidas com porosidade variando de 62 a 87 %-vol, o que corresponde a densidades relativas entre 0,13 e 0,38. Essas esponjas foram utilizadas para a verificação de modelos, tais como de Mackenzie, de Boccaccini e de Gibson e Ashby, que relacionam a porosidade ou a densidade com os módulos elásticos da cerâmica porosa. Os módulos elásticos de Young, de cisalhamento e a razão de Poisson foram caracterizados através da técnica de ressonância mecânica de barras. Essa técnica permitiu avaliar os valores dos módulos elásticos mesmo com o material tendo macroestrutura celular. Os resultados permitiram verificar qual dos citados modelos oferece melhor descrição do comportamento do módulo elástico em função da porosidade das esponjas cerâmicas. Palavras-chave: cerâmica porosa, gelcasting, módulo elástico, ressonância de barras, alumina. Abstract Broad porosity range can be obtained in ceramic foams employing the gelcasting

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“…Nevertheless, derivation of upper and lower limits only is still not satisfying. Recently, finite element methods (FEM) have been used extensively to simulate the elastic properties of composite materials based on 2D or 3D reconstructions of real microstructures [22][23][24][25][26]. The required computational efforts, however, are quite demanding, including imaging of the real microstructures in the first place, reconstruction of the digital images and finally FEM simulation of the elastic behavior.…”

Section: Introductionmentioning

confidence: 99%

Analytic approximations for the elastic moduli of two-phase materials

et al. 2017

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Based on the models of series and parallel connections of the two phases in a composite, analytic approximations are derived for the elastic constants (Young's modulus, shear modulus, and Poisson's ratio) of elastically isotropic two-phase composites containing second phases of various volume fractions, shapes, and regular distributions.Comparison with a plentitude of finite element simulations and numerous previous experimental investigations shows a large consistency between the results and the analytic expressions derived, confirming the adequacy of the present approach. Compared with previous classical models, the present model has several advantages, including its simplicity, accuracy of prediction, and universal applicability.

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Elastic moduli of model random three-dimensional closed-cell cellular solids

Cited by 423 publications

References 26 publications

Mechanical properties of highly porous PDLLA/Bioglass® composite foams as scaffolds for bone tissue engineering

Mechanical properties of highly porous PDLLA/Bioglass® composite foams as scaffolds for bone tissue engineering

Relação entre porosidade e os módulos elásticos de esponjas cerâmicas produzidas via "gelcasting"

Analytic approximations for the elastic moduli of two-phase materials

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